A subsequence characterization of sequences spanning isomorphically polyhedral Banach spaces

• Autorzy: G. Androulakis
• Języki publikacji: EN

Abstrakty

EN

Let (x_n) be a sequence in a Banach space X which does not converge in norm, and let E be an isomorphically precisely norming set for X such that (*) ∑_n |x*(x_{n+1} - x_n)| < ∞, ∀x* ∈ E. Then there exists a subsequence of (x_n) which spans an isomorphically polyhedral Banach space. It follows immediately from results of V. Fonf that the converse is also true: If Y is a separable isomorphically polyhedral Banach space then there exists a normalized M-basis (x_n) which spans Y and there exists an isomorphically precisely norming set E for Y such that (*) is satisfied. As an application of this subsequence characterization of sequences spanning isomorphically polyhedral Banach spaces we obtain a strengthening of a result of J. Elton, and an Orlicz-Pettis type result.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 127
• Numer: 1
• Strony: 65-80

Daty

wydano

1998

otrzymano

1996-10-29

poprawiono

1997-06-09

Twórcy

autor

G. Androulakis

• Mathematical Sciences Building, University of Missouri-Columbia, Columbia, Missouri 65211, U.S.A.

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